Solve for $x$ and $y$ using elimination. ${6x-6y = 24}$ ${-5x-5y = -60}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-6$ ${30x-30y = 120}$ $30x+30y = 360$ Add the top and bottom equations together. $60x = 480$ $\dfrac{60x}{{60}} = \dfrac{480}{{60}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {6x-6y = 24}\thinspace$ to find $y$ ${6}{(8)}{ - 6y = 24}$ $48-6y = 24$ $48{-48} - 6y = 24{-48}$ $-6y = -24$ $\dfrac{-6y}{{-6}} = \dfrac{-24}{{-6}}$ ${y = 4}$ You can also plug ${x = 8}$ into $\thinspace {-5x-5y = -60}\thinspace$ and get the same answer for $y$ : ${-5}{(8)}{ - 5y = -60}$ ${y = 4}$